Problem: What number makes this equation true? $557 = 106 + $
Explanation: $557 = 106 +{{?}}$ ${106}$ ${557}$ $+?$ Let's start by adding hundreds to ${106}$ until we get as close to ${557}$ as possible without going over ${557}$. $\begin{aligned} {106} +100}=206\\\\ {206} +100}= 306\\\\ {306} +100}= 406\\\\ {406} +100}= 506 \end{aligned}$ If we add $4 \text{ hundreds}}$, or $4 00}$, we reach $506$. We cannot add any more hundreds without going over ${557}$. ${106}$ ${557}$ ${506}$ $+400$ Next, let's add tens to $506$ until we get as close to ${557}$ as possible without going over ${557}$. $\begin{aligned} 506 +{10}=516\\\\ {516} +{10}= 526\\\\ {526} +{10}= 536\\\\ {536} +{10}= 546\\\\ {546} +{10}= 556 \end{aligned}$ If we add ${5 \text{ tens}}$, or ${50}$, we reach $556$. We cannot add any more tens without going over ${557}$. ${106}$ ${557}$ ${506}$ ${556}$ $+400$ $+50$ Finally, how many ones should we add to $556$ to get to ${557}?$ $556 +{1}={557}$ ${106}$ ${557}$ ${506}$ ${556}$ $+400$ $+50$ $+1$ We added $4 \text{ hundreds}}$, ${5 \text{ tens}}$, and ${1\text{ one}}$ to ${106}$ to get to ${557}$. $4 00}+{5 0}+{1}={451}$ ${106}$ ${557}$ ${506}$ ${556}$ $+400$ $+50$ $+1$ $+451$ $557 = 106 +{451}$